Micromagnetism and microstructure of hard magnetic materials

High-performance magnetic materials are based on outstanding intrinsic magnetic properties and optimized microstructures and alloy compositions. The interactions between these three parameters in general are rather complex and cannot be treated explicitly by the theory of micromagnetism. Instead numerical methods have to be applied in order to determine the characteristic properties of hysteresis loops. Within the framework of computational micromagnetism (nanomagnetism) using the finite-element method the coercive fields of different types of grain ensembles have been determined. In the case of nanocrystalline composites the roles of grain size, exchange and dipolar coupling between grains will be discussed in detail. It is shown that, in sintered magnets, large coercivities require magnetic de-coupling between the grains, whereas regions with exchange coupling reduce the coercive field drastically, but, however, increase the remanence., Nanocrystalline composite materials with remanence enhancement and high coercivities are shown to require soft grains with diameters of twice the wall width of the hard magnetic phase. For an amount of 50% alpha-Fe coercivities of mu(0)H(C) = 0.75 T, a remanence of 1.5 T and an energy product of (BH)(max) = 450 kJ m(-3) are expected. A quantitative analysis ct the numerical results for He and the remanence leads to logarithmic dependences on grain size.